
under the assumption \(K(x,h)=K(x,-h)\)  and \(K(x,h) \asymp |h|^{-d-\alpha }\)  for
all \(x\)  and \(h\)  where
\(\alpha \in (0,2)\)  is fixed. Note that this class includes the case \( \mathcal {L}u =-(-\Delta )^{\alpha /2} u\)  and versions with bounded measurable coefficients.
As [1]} does, the article [2]} establishes a priori estimates in
Hölder spaces. Results like lem:growth have been obtained for
operators in the case \(K(x,h) \asymp |h|^{-d-\alpha }\)  also for nonlinear problems, cf. [3]}, [4]}
and [5]}.
